24 citations · 53 across the 11 of their papers we have counts for
5 papers · 1 filter
Shuffle algebras, lattice paths and Macdonald functions
Alexandr Garbali, Ajeeth Gunna
We consider partition functions on the square lattice with the local Boltzmann weights given by the -matrix of the quantum algebra. We i…
A -deformation of the 2d Toda integrable hierarchy
Jean-Emile Bourgine, Alexandr Garbali
A -deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra to the quan…
The -matrix of the quantum toroidal algebra in the Fock module
Alexandr Garbali, Jan de Gier
We propose a method to compute the -matrix on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algeb…
Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
Luigi Cantini, Alexandr Garbali, Jan de Gier +1
We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corol…
A new generalisation of Macdonald polynomials
Alexandr Garbali, Jan de Gier, Michael Wheeler
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters and polynomial in a further two parameters $…